The blaze was reported at South 24th and East San Antonio streets around 5:45 a.m. and was controlled as of about 8:15 a.m., according to San Jose fire Capt. Rob Brown.
The person staying in the trailer, a man in his 50s, suffered minor smoke inhalation and was treated at the scene.
A small dog living in the trailer has not yet been accounted for, according to Brown.
"We don't have any evidence that the dog died in the fire but we can't rule it out either," Brown said.
Firefighters called a second alarm due to the trailer's proximity to a commercial building, according to Brown.
"The trailer backed up to another commercial building -- that was a potential fire hazard for us, so we called a second alarm to get extra crews to make sure we didn't have any fire spread," Brown said.
The flames were contained to the trailer, which is considered a total loss, he said.